UL ÆW?OMF*«WMb*«WU d? vk blf «cë U?Nd s nk b U? WMb d w

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1 µ ± µøâ µ µ doj«êb*«w öb«, ±  XOu, ÂuK F««u œëb : eef«b pk*«wfu WK doj«êb*«w öb«xou «u œëb vhdb*«sld«b w WOMI«Ë ÂuKFK eef«b pk*«wmb, UeOuO'«Ë pkh«àu bnf WœuF«WOdF«WJKL*«U d«èub WOL «UÎ{d WO?öù«WFdA«w öb«df ÆhK*««c U?Ë_U bo?i?«v YO?Ë, œb? U?Ë UNË rk?*«uo? w Ê U?L? Æp? sj U? ö?b«u??ë»u?? bm W??b«Íd?% VË s U?Iô«ÊS? wuuë fl?a«l«u0 d?u? Wö? öb«u?ë_ ö?: XË ŸU?«sJ1 ö? ö?b«xë u?œ s d?o?g d? v ÊUJ WMb qj ÊuJ Ê V q ji Wd U?N U vk U WMb w Îö à U UNKF? ô jo w sj r U U?N W:U)«öB«U?Ë_ UÎU ÆXOu««u YO? Wb XOu?««u U?OF? bb% d Ë_ - Y?««c w «cë ö?b«xo??«u? «b?: bm Êb?LK œëb? l{ë t?ö? s sj1 W?IO?œ ± Ë»d?G«Ë da?«wu&«w W?O?u W?I?Oœ ± t?u UO?F*«ÆWœuF«WOdF«WJKL*«w p Ë»uM'«Ë ULA«wU&«w WOu W!b I! w Æ ± qj, Êb*«iF w UFu«Yb(«Xu«w w«d?lf«lu«u bi d lu Í Ë bk«w wozd«lu'«ë b*«vk? blf öb«uë»u µ

2 vhdb*«sld«b w Æ Ud«WMb* wo«dô«jdlk wo{u r Æ ± qj Æ ± ± ± Ud«WMb* qua«wo«dô«jd<«: bb*«

3 doj«êb*«w öb«xou «u œëb öb?«uë»u? Ê wmf U2,Èd?_«l«u'«Ë b?u*«lu? s dem«ig UL ÆW?OMF*«WMb*«WU d? vk blf «cë U?Nd s nk b U? WMb d w ÎU?F? UN?«d_ U??UM ÊuJ Ê Ëd?CU fo WMb*«e?d* ö?b«u?ë»u? Ê Ë W«œ œu VË»U?(«vK œulô«ë rkf«âbi lë «c?,îuc WMb*«Ác dj b?*«ë lu'«u«bf b?«u«wmblk XOu?««u bb% WO?HO `O{u? b WKO?HJ«q«U?«r ö?b«uë»u?( ld?l WM?b*«ed? v Ë w?ozd«d? bi?ë Æ do?? WMb? sl{ X?U Ê Ë b?o?f?«oumlk W?UM? UUO??«l{u ö?: b?u?»u??? u u?_«ë WKJA*«Ác?N q??_«q(«ê ò t?b U? ± œu? W?M?U öb«xo?«u? wu»u?ë WM?b*«dA W??MU fl?a«ëd?ë d?h«tu?œ q»d?g«w d?h«uœ qf? b q(««c q? Ê YOË å WMb*d?G»U??:_ U?:u?B? d?u?? Ê«_«ŸU?L b?f? wkb s ö?: b??h b?ë wkf?h«b Ë W«œ œu? Vu U2 Íb d?o ± œu Ád? Íc«q(«ÊS wu?uë «c_«æ doj«êb*«w öb«bo«u bb tu«v Íc«XOu«U U«d* 5œU?F*«V?? lu*«vk b?l??f W??U W«b d?o?g? d?f?«ë ud«ud Ê The ru ÎUuM b?b w«wo*u?f«.ëui?«s U?LN?OK ub?(«sj1 w«ë 5OU?«: df«j q9 φ YO Astronomical Almanac ÍËU d*u df«j w b«ë W œ cos 2φ cos 4φ ÍËU d*u ud«j w b«ë W œ cos φ cos 3φ cos 5φ dü ÊUJ s U?Iô«d vmf0 Ë d?ë u wd Í 5 UIô«ÊS? wuuë Ëd U?Ë»U s UMMJ1 U2 U? bu Ë d*u «u WOU?M Wb UNU? sj1 Âb? WOuO«tU?O w ÊUù«Ê YOË W?OM tou»d_ Wb f?laëdë U w«u«vd?i l WIOœ»d_ W?OM.ËUI«lOL? ÊS WOM WIOœ»d?_ WU«vK d?h«ë»d?g*«wö?: w UL? ö?b«xë `UB ÊU «d??«êub?i Ë œu Æ ÊU «dô«êubim«ë œue«woklf Uu{Ë wdf wu«u*«ë,w«u«

4 vhdb*«sld«b w w «c WOU Ë WIO?œ µë WF«d«WU«dH«ö?B Ê«_«XË qb öl XË qb wu?«qja?u `?B U?N?d?I r.ëu?i?«w?u? bmë wü«vu?(«ê«_«xu W?MU `O?: fjf«ë WIO?œ µë WF«d«W?U«d?H«öB Ê«_«Ë WIOœ µë WœU«WUdG*«öB Ê«_«XË qb öl»dg*«öb öb Ê«_«XË qb wu?«qjau `B UN?dI r.ëui«wu? bmë WOU ÆWIOœ Ë WœU«WUdG*«U ½UO³#«q OK% p Ë Mica 1.5 ZUd «b??U fl?aëdë Ëd?A UU? ql? - 5IOœ U?NœUe UO«bù«dOOG -Ë, µ «um b?f UU qlf uœ w dog vk b fl?aëd Ë Ëd UË w doog Í Ê YO? WOu wë WDI qj q«d Àö v UUO«qOK%Ë W«œ roi - bië, öb«uë :wuu Æ df«j U l ji ud«j w dog«± Æ ud«j U l ji df«j w dog«æîuf ud«ë df«wd w dog«w«oum*«`{u WDd ql?f p Ë WOFd*«WDIMU WDO;«W?IDM*«WODG - «cnë ÆÊ«ô«XË UNO dog q Wd?F* UU?(«UNOK XI? WO?{ ô«dj«vk WOz«uA? l«u b? c - v UMKI??«U?LK qi b?(««c Ê `C«b?IË.ËU?I?«œ«b? b?m tu?«d? V b? b?(«w WO?u W?IO?œ da? W? Ê bë b?ië ÆWO?UF«W?O{d?F«uD)««oUM flaëd Ë Ëd d him Ë be wj Wœu?F«WOdF«WJKL*«w q:uh«5u?&ô«w p Ë 5?OM? 5?I?O?œ v W?OM W?I?O?œ s W?«b«l«u? e?«d? s 5U?&ô«w W?Ou? W?I?Oœ 5öË b?«ë v b?(««c qb U?LMO wd?g«ë wd?a«àb? w«oum*«ë Êb?LK? Èd.ËU?I œu? V?u «cë, wum'«ë wu?l?a«æd Ë 5IOœ d UNO

5 π doj«êb*«w öb«xou «u œëb Ëd»U?( p Ë Èd v W?IDM s Xu«dOG W?OHO?Ë ZzUM«iF d? ÆÈd v WIDM s UIô«bM flaëdë Æ ± Ëb uou π qd«± dum ÎôUL : ÎU d : µ: ± : ÎôUL : ÎU d : µ: ± :± ÎôUL : ÎU d π: π : ± : ÎôUL µ:± ÎU d : µ: µ ± : ÎôUL : ÎU d :µ µ: ± :±µ ÎôUL : ÎU d : µ : ± ± : d?o?g w?«œëb(«`{u U?d«WMb* W U? ql? - bik b?(««c `O?{u?Ë l öb«u?ë_ Ë«b l{ë V v? `{u W U)«Ác ÆÊ«_«XO?u UbM Ud«WM?b? œëb? sl??{ s w bb?? Ë«b? v ÃU???% w«oum?*«ê rkf«æ ± ± ± Ud«WMb* qua«wo«dô«jd<«w WuLA*«wO«d?ô«jD<«wDG W?OUMB«U?LôU UdK W U? `{u qja«u?ë_ bb'«b?(«sl?{ à bm w«oum*«`{u? qja«ul?mo Ud«WMb* fh X?b?????«W??«b«Ê kö*«së,b??(«ã U?? li w?«oum*«ë ö??b«ë W œ wë ÈdI«Â.u?I w Wb?*«Ud«WMb* df«ë ud«ud ÆÎôUL WIOœ Ë W œ Ë ÎUd WIOœ Ud«WMb? dud U?OKF«W?ON«U?N?ML{ oum w b?(«ã U? li w«oum*«qja«s `{«Ë u U?L oum wë w?o«d?ô«ud«wmb jd? sl{ Æ Ëb öb«uë w Ud«WMb ed l Ê sj1ô

6 vhdb*«sld«b w ee?f«b? pk*«wmb, U?C?H«Àu b?nf? : bb*«ud?«wmb* WOzU?C u?: b? l? w«oum*«5? rd«vk W??{u*«jIM«q«œ oum?*«wo?mi?«ë ÂuKFK s Xu«U?N?O d?o?g w?«oum*«w jim«u?nod?g w«oum*«u?lmo XO?u«U? Æ XOu«U b à U UN Í WOM 5IOœ v WIOœ Æ qj

7 ± doj«êb*«w öb«xou «u œëb oum?*«lo?l?? wë XO??u??««u?? b? sl??{ à bm ô w?«oum*«`{u? r Æ WLË ÊUM «bu Ud«WMb* wo«dô«jd<«w WuLA*«Æ qj

8 vhdb*«sld«b w Æ Ud«WMb* wo«dù«jd<«sl{ W b*«oum*«if Æ Ëb d F«j WOU WIOœ W œ µ µπ µπ ±µ µ µ µ ±± µ± µ µ µ µµ π u D«j WOU WIOœ W œ ± µ π µ ± µ π µ µπ µ W Mb*«ÊUM W UDK W MOOF«WKO'«W{u Ø WCu W ULF«Ëd«U d W L do Ë XO W OULF«U O$u ²#«Ë W $ö )«b?f,un? b ql?ë XO?u?««u W?O?{d l{ë d? Ë_Ë W?«b«Ác w - p Ë U?LA«vB? v «u?ô«j s b2 ru?f«w WHK? l?«u b? W«œ «U? W?d?F? tk?«u? Ê U?N r?o? XI? Ê w?«ë, µ «um b?f b(««c WL?O XU bië tb? s öb«uë w Ue«d? l Êb*««d XU w W?Ou W?IO?œ 5öË b?«ë Ë»dG«Ë d?a«wu&«w W?Ou? WI?Oœ d?a W? WL?OI«Ác oo?d sj1ë WœuF?«WOdF«W?JKL*«w p Ë»uM'«Ë UL?A«wU&«Æ df«ud w WœuF«l da w«ëb«lol vk :wk U v bb'«w«b«ác s hkë ö?bk.ëu?i œ«b? w ŸËd?A?«q? WMb? Í W?U?* W?«œ œu?ë W?O?L ± bb'«b(«ë U?OF*««c ood v WU? WMb*«Ác XU «U Wd?F bn p Ë ÆUNOK

9 doj«êb*«w öb«xou «u œëb vk VKGK? p Ë UU(«œ«b? w ldl WMb*«e?d c U?«d V ÆWMb*«w wozd«lu'«lu s dem«ig WMbLK wki*«w«dlf«lu«vu t?s b(«u?nok odm YO? WMbLK wk?i? jod œu?ë WU w ÁcN Êu?JË Â_«WMb*U WI?K bb Êb? UA r U/ Ë U?NCF? WMb*«U?B«Âb do w Ê RË UË_«q«b ô w p Ë öb«.ëu?i œ«b bm WOöI«WMb*«ÆÊ«_«XË d¹b IðË dj ý q?l?*«wmh«rb«r tk«oo?u ôu u?b«ácn Ãd??O sj r ql?f««c Ê ÆWOMI«Ë ÂuKFK eef«b pk*«wmb0 UCH«Àu bnf q s WOzUCH«uB«w l ł«d *«wu?«wö?ù«wjk?h«d9r*«, ö?b«xo?«u?»u??, ±, Xu? b?l???, œu? ± Æ ± Êœ _«,åwoöù«wfda«w WOJKH«UIOD«ò U.S. Government Printing Office, The Astronomical Almanac, Washington, D.C., , ± ± U d«w Mb* qu?a«w?o«d?ô«j D<«, U d«w Mb? du D U?OKF«W O?N«Æ ± Mica 1.5 ZUd MICA 1.5 is a product of the Astronomical Applications Department of the U.S.Naval Observatory, Willmann-Bell, Inc.,

10 vhdb*«sld«b w Time Limits of Prayer in Saudi Arabia ZAKI ABDUL REHMAN MUSTAFA King Abdulaziz City for Science and Technology, Riyadh, Saudi Arabia ABSTRACT. The prayer call is of vital importance in the Islamic sharea'a (rules), since prayers cannot be started before that. Prayers times are related to the position of the place (i.e. latitude and longitude) and hence related to the position of the Sun in the sky. There is a prayer time table for each zone, and different zone's time table is not applicable to another unless it is very close to the first one. This paper represents a time limit boundary calculated for the first time. This new time limit is 16' (minute of arc) in the East or West directions and 31' in the North or South directions in the Kingdom of Saudi Arabia.

Keywords: One-Way ANOVA, GLM procedure, MIXED procedure, Kenward-Roger method, Restricted maximum likelihood (REML).

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